Diffusion Synthetic Acceleration of Discontinuous Finite Element Transport Iterations

Adams, Marvin L.; Martin, William R.

doi:10.13182/nse92-a23930

Cited by 59 publications

(40 citation statements)

References 10 publications

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“…The low-order equations are discretized by the lumped bilinear-discontinuous (BLD) method [26,27]. The BLD approximation of the partial scalar fluxes in the (i, j)-cell is…”

Section: Discretization Of the 2d Nwf Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Anistratov¹,

Constantinescu²,

Roberts³

et al. 2007

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“…The low-order equations are discretized by the lumped bilinear-discontinuous (BLD) method [26,27]. The BLD approximation of the partial scalar fluxes in the (i, j)-cell is…”

Section: Discretization Of the 2d Nwf Methodsmentioning

confidence: 99%

“…For a structured mesh, in which an interface is composed of two and only two faces, interface conditions are to simply enforce continuity of face-average current and face-average scalar flux: 26) for interface of faces iω and i ω .…”

Section: Interface Continuity Conditionsmentioning

confidence: 99%

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Anistratov¹,

Constantinescu²,

Roberts³

et al. 2007

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“…Concurrently, there was a great deal of investigation into diffusion synthetic acceleration (DSA) in several geometric settings of the transport equation [2,4] that preconditioned simple iterative methods for various discretizations of the hyperbolic component of the transport equation. By 2002, Adams and Larsen [1] had very nicely summarized what was known by then in applying iterative methods for particle transport problems.…”

Section: Brief Overview Of Previous Effortsmentioning

confidence: 99%

“…Yet while over the years there have been several numerical investigations (e.g. [11,[17][18]) into the numerical behavior of various approximations to (1), the literature devoted to preconditioned Krylov methods for the 1-D spherically symmetric case is much sparser (see [2], Appendix A)…”

Section: Brief Overview Of Previous Effortsmentioning

confidence: 99%

Discontinuous 1-D Spherical Transport Solvers using Diffusion Preconditioner and Iterative Methods

Machorro

2011

J Fusion Energ

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Using discontinuous Galerkin finite-element methods to solve the hyperbolic components of the transport operator in the 1-D spherically symmetric case, the convergence behavior of various iterative methods are compared and evaluated. Diffusion synthetic accelerator, a preconditioner based on the diffusion approximation to the transport equation, is presented formally for this geometry for the first time. Compared with classical, finite-difference like methods (diamond difference methods), it is found that DG diffusion based preconditioners performed extremely well in resolving problems with strong scattering effects and material discontinuities.Keywords Neutron transport equation Á Iterative methods Á Integro-differential operator Discontinuous Galerkin Methods with Isotropic ScatteringThe Boltzmann operator considered here iswhere r t C r s C 0. The notation S½w r s ðrÞ Z þ1 À1 wðr;lÞ dl 2 ¼ r s ðrÞuðrÞ ð 2Þ may be used on occasion where the scalar flux is defined as uðrÞ ¼ Z þ1 À1 wðr;lÞ dl 2 :The streaming-collision operator T ¼ B À S can be written as T ¼ j Á r þ r t where j ¼ ðl; 1Àl 2 r Þ: The Boltzmann transport equation (BTE) problem properly stated is as follows: Given a domain D ¼ ½0; 1 Â ½À1; 1 in (r, l)-space, and source term q(r), find a solution w(r, l) such thatNote that in many of the examples it will be commonly assumed that r t , q, and r s are all isotropic (independent of l), but in all cases these quantities are non-negative. Brief Overview of Previous EffortsIn 1973, Lesaint and Ravaint [12] produced one of the seminal studies of the convergence properties of the discontinuous Galerkin (DG) method as applied to the nonscattering constant coefficient 2-D Cartesian transport equation

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“…However, with the emergence of new types of reactors with more intricate geometries or more severe flux transients, the motivation to pursue more accurate numerical simulations is calling for finer geometrical details, increased number of energy groups and more angles or moments in the transport equation. The finite element method (FEM) since as early as the mid 70's, [15], [16], [17] , which had been introduced in nuclear engineering and gradually obtained more attention [18], [19], is of special interest to us because it provides an efficient way to refine the mesh non-uniformly while delivering accurate solutions.…”

Section: Finite Element Methodsmentioning

confidence: 99%

Approximation of The Neutron Diffusion Equation on Hexagonal Geometries Using a h-p finite element method

Moawad¹

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Diffusion Synthetic Acceleration of Discontinuous Finite Element Transport Iterations

Cited by 59 publications

References 10 publications

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Discontinuous 1-D Spherical Transport Solvers using Diffusion Preconditioner and Iterative Methods

Approximation of The Neutron Diffusion Equation on Hexagonal Geometries Using a h-p finite element method

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